Generally, no - a mechanics lien will not cure any sort of unpaid registration fees. Rather, a mechanics lien's purpose is to recover amounts owed and unpaid for work that's performed which permanently improves the project property. And, when construction debts go unpaid, a lien may be the most powerful tool available for recovering payment.
For more background on how mechanics liens work, I think these resources will be valuable:
- What is a Mechanics Lien? | Mechanics Lien 101- How Do Mechanics Liens Work? 17 Ways a Lien Gets You Paid